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Homework Set 2
Due Wednesday, 07/06
Problem 1
A wave on a string has an amplitude of 1.5cm, a period of 0.12 seconds, and a
wavelength of 1.1 meters.
a.
What is the wave's frequency, angular frequency, wave number and wave speed?
b.
If the string is under tension of 5.0N, what is its mass per unit length, in grams per
meter?
c.
If the tension in the string changes to 10.0N but the frequency of the wave remains
the same, what is its new wavelength?
Solution:
a.
The frequency, angular frequency, wave number and wave speed are
b.
We know the wave speed from part (a) and are given the tension, so we can solve for
the mass per unit length:
c.
First, determine how the wavelength depends on the tension, if the frequency is held
fixed:
The wavelength is therefore proportional to the square root of the tension.
The tension
is doubled, so the new wavelength is
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View Full Document Problem 2
A string with mass per unit length
μ
= 10.0g/m is tied down on one side, and runs over a
pulley on the other side, 0.30 meters away.
The end that runs over the pulley is attached
to a 1.5 kilogram mass.
Assume that the end of the string that is tied down and the point
that runs over the pulley cannot move, but the piece between these points is free to
oscillate.
a.
What is the string's fundamental frequency?
b.
Now this system is placed in an accelerating elevator.
The 3rd harmonic frequency is
measured to be 204 hz.
Is the elevator accelerating up or down?
What is its
acceleration?
Solution:
a.
In the fundamental mode, half a wavelength fits on the string between
x = 0
and
x = L
.
Therefore, the wavelength is 0.60m.
The wave speed is
The frequency of the fundamental mode is then
b.
To figure out the acceleration, we need to know the effective gravity inside the
elevator.
We are given the frequency of the 3rd normal mode, which is equal to 3 times
the frequency of the 1st mode.
Use this to determine the wave speed:
Since the apparent acceleration due to gravity inside the elevator is higher than
g
by
1.3m/s
2
, we know that the elevator is accelerating upward at 1.3m/s
2
.
Problem 3
Two strings with different masses per unit length are connected together and held at a
tension of 50
N
:
An wave with an amplitude of 2.50cm and a frequency of 60.0 hz is incident from the
left.
The waves on the lefthand string are observed to have a wavelength of 30.0cm,
while those on the righthand string have a wavelength of 20.0cm.
a.
What is the mass per unit length,
μ
1
, of the left string?
What is the mass per unit
length of the right string?
b.
What is the amplitude of the transmitted waves on the right string?
c.
What is the transmission coefficient?
What is the reflection coefficient?
Solution:
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This note was uploaded on 09/19/2011 for the course PHYS 1C taught by Professor Smith during the Spring '07 term at UCSD.
 Spring '07
 Smith
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